Peculiar motions of Abell clusters in compact groups

An estimator (measure) of the observed pair redshift velocity variance, $E(\sigma_\text{v}^{2})\,=\,\sigma_\text{R}^{2}\,-\,\frac{1}{2}\sigma _\text{T}^{2}$, is evaluated from the observed separation vectors of Abell clusters, resolved into a component in (a) the redshift direction, R, and (b) the plane of the sky, $T\,=\,\sqrt{{x}^{2}+{y}^{2}}$, analysed with allowance for edges in the survey regions. Several statistical samples are studied, including rich groups containing five or more clusters identified individually by a procedure that applies linkage of separation vectors of length $\leqslant42\,\text{Mpc}\,({H}_{0} = 100\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ followed by a 3σ statistical test on consecutive differences of ordered coordinates. Compact groups of clusters with cluster–cluster separations ≃ 10 Mpc each have an observed rms pair redshift velocity dispersion ${\sigma }_\text{v}\,\simeq\,2100\,\text{km}\,\text{s}^{-1}$ (above zero at the 2σ, 98 per cent confidence level), corresponding to a physical rms redshift velocity dispersion of clusters with respect to the group barycentre ${\sigma}_\text{v0}\,\simeq\,1200\,\text{km}\,\text{s}^{-1}$, suggestive of large peculiar motions. The velocity dispersion is smaller for looser groups, and ${\sigma }_\text{v}\,\simeq\,0$ for groups with cluster–cluster separations ≃ 21 Mpc (the scalelength of the two-point correlation function of Abell clusters), consistent with unperturbed Hubble flow, small infall, and/or small peculiar motions. The derived rms error of $E(\sigma_\text{v}^{2})$ for the two identified rich compact groups, $\simeq\,0.5\,E(\sigma_\text{v}^{2})$, and for the other samples, is the quadrature sum of the contributions by the intrinsic uncertainty of the estimator, errors in cluster redshifts, anisotropic geometrical structure, and the enhancement of cluster richness counts by projected neighbours on the sky.